What flavours of Linear Logic are algebraizable?

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I am a theoretical linguistics student and I have been working in the last few years on an improved model of natural language semantics, but I am missing a final mathematical insight in order to wrap up my work.

The theory implements the intuitionistic multiplicative fragment of Linear Logic, i.e. LL($\otimes, \multimap$) and I was asking myself whether it is algebraizable or maybe, before considering that, whether one of the proposed interpretations of LL($\otimes, \multimap$) (quantales, GoI, Petri nets, game theory and possibly others) is considered algebraic. My final goal is working with sets of equations over an algebraic structure interpreting LL($\otimes, \multimap$).

Please tell me if you need any more information.